The Judaism when the Talmud was written was a fanatically proselytizing sect, as is clear if you read the talmud. They created seed outposts all over the Roman empire of new converts, as they sought (and obtained) special dispensation to be the only religion allowed to proselytize in ancient Rome and they had an active missionary service travelling all over the world seeking converts. These missionary efforts were quite successful, spreading judaism to the far reaches of the Roman Empire, creating enclaves of newly converted Jews in the major cities of the Western world. It is these enclaves that were most receptive to Christianity during its initial expansion, and in that period when Christianty was considered another sect of Judaism, the Christians also used the special dispensation given to Jews to gain converts. This created tension, where some of the Jews complained to the Roman authorities that these Christian Jews were not real jews and thus should not be allowed to proselytize under the dispensation alloted to jews. This information also forms the backdrop that helps understand early Christian history. For example, in the first apostolic council recorded in acts, what was meant by saying "Moses is preached in all the synagogues" when referring to new converts in Corinth, Rome, and Ephesus. It is because those new converts were either fully converted jews, themselves converted a few generations previously by Pharisee missionaries, or they were in some other stage of the conversion process, and so they, too, met in Synagogues, even in places like Ephesus, and thus the early Christian missionaries just went from Synagogue to Synagogue all over the Roman Empire, winning over the descendents of converts in communities that were previously won over to judaism.
The Pharisee missionary work is also mentioned in the New Testament, when Christ accuses the Pharisees, saying "You travel over land and sea to make one convert and when you do, he is twice the son of hell that you are."
This missionary program was so successful that much of the Talmud was written by the children of new converts, in new communities all over the Roman Empire. Rabbi Hillel's famous retort to a man demanding to know the meaning of the Talmud while standing on one leg was in a debate that was attempting to convert his (gentile) questionner to judaism. In fact the background to many of the famous passages in the talmud were attempts at conversion and evangelization. Knowing that is an important part of understanding these passages. These jewish communities also provided sancturary to fleeing Jews after the Romans expelled them from Palestine in the wake of the third revolt - they were taken in by the descendents of new converts created by Pharisees, and these cities became the seed communities of jews in Europe and North Africa.
But it is true that modern Judaism does not try to convert others and has become a racial identity as much or moreso than a religious identity, however this was not the case for those rabbis when the mishna was compiled or when the oldest portions of the Gemara were first written.